[petsc-users] Advice on improving Stokes Schur preconditioners
David Nolte
dnolte at dim.uchile.cl
Mon Jun 12 14:20:07 CDT 2017
Ok. With "-pc_fieldsplit_schur_fact_type full" the outer iteration
converges in 1 step. The problem remain the Schur iterations.
I was not sure if the problem was maybe the singular pressure or the
pressure Dirichlet BC. I tested the solver with a standard Stokes flow
in a pipe with a constriction (zero Neumann BC for the pressure at the
outlet) and in a 3D cavity (enclosed flow, no pressure BC or fixed at
one point). I am not sure if I need to attach the constant pressure
nullspace to the matrix for GMRES. Not doing so does not alter the
convergence of GMRES in the Schur solver (nor the pressure solution),
using a pressure Dirichlet BC however slows down convergence (I suppose
because of the scaling of the matrix).
I also checked the pressure mass matrix that I give PETSc, it looks correct.
In all these cases, the solver behaves just as before. With LU in
fieldsplit_0 and GMRES/LU with rtol 1e-10 in fieldsplit_1, it converges
after 1 outer iteration, but the inner Schur solver converges slowly.
How should the convergence of GMRES/LU of the Schur complement
*normally* behave?
Thanks again!
David
On 06/12/2017 12:41 PM, Matthew Knepley wrote:
> On Mon, Jun 12, 2017 at 10:36 AM, David Nolte <dnolte at dim.uchile.cl
> <mailto:dnolte at dim.uchile.cl>> wrote:
>
>
> On 06/12/2017 07:50 AM, Matthew Knepley wrote:
>> On Sun, Jun 11, 2017 at 11:06 PM, David Nolte
>> <dnolte at dim.uchile.cl <mailto:dnolte at dim.uchile.cl>> wrote:
>>
>> Thanks Matt, makes sense to me!
>>
>> I skipped direct solvers at first because for these 'real'
>> configurations LU (mumps/superlu_dist) usally goes out of
>> memory (got 32GB RAM). It would be reasonable to take one
>> more step back and play with synthetic examples.
>> I managed to run one case though with 936k dofs using:
>> ("user" =pressure mass matrix)
>>
>> <...>
>> -pc_fieldsplit_schur_fact_type upper
>> -pc_fieldsplit_schur_precondition user
>> -fieldsplit_0_ksp_type preonly
>> -fieldsplit_0_pc_type lu
>> -fieldsplit_0_pc_factor_mat_solver_package mumps
>>
>> -fieldsplit_1_ksp_type gmres
>> -fieldsplit_1_ksp_monitor_true_residuals
>> -fieldsplit_1_ksp_rtol 1e-10
>> -fieldsplit_1_pc_type lu
>> -fieldsplit_1_pc_factor_mat_solver_package mumps
>>
>> It takes 2 outer iterations, as expected. However the
>> fieldsplit_1 solve takes very long.
>>
>>
>> 1) It should take 1 outer iterate, not two. The problem is that
>> your Schur tolerance is way too high. Use
>>
>> -fieldsplit_1_ksp_rtol 1e-10
>>
>> or something like that. Then it will take 1 iterate.
>
> Shouldn't it take 2 with a triangular Schur factorization and
> exact preconditioners, and 1 with a full factorization? (cf. Benzi
> et al 2005, p.66,
> http://www.mathcs.emory.edu/~benzi/Web_papers/bgl05.pdf
> <http://www.mathcs.emory.edu/%7Ebenzi/Web_papers/bgl05.pdf>)
>
> That's exactly what I set: -fieldsplit_1_ksp_rtol 1e-10 and the
> Schur solver does drop below "rtol < 1e-10"
>
>
> Oh, yes. Take away the upper until things are worked out.
>
> Thanks,
>
> Matt
>
>>
>> 2) There is a problem with the Schur solve. Now from the iterates
>>
>> 423 KSP preconditioned resid norm 2.638419658982e-02 true resid
>> norm 7.229653211635e-11 ||r(i)||/||b|| 7.229653211635e-11
>>
>> it is clear that the preconditioner is really screwing stuff up.
>> For testing, you can use
>>
>> -pc_fieldsplit_schur_precondition full
>>
>> and your same setup here. It should take one iterate. I think
>> there is something wrong with your
>> mass matrix.
>
> I agree. I forgot to mention that I am considering an "enclosed
> flow" problem, with u=0 on all the boundary and a Dirichlet
> condition for the pressure in one point for fixing the constant
> pressure. Maybe the preconditioner is not consistent with this
> setup, need to check this..
>
> Thanks a lot
>
>
>>
>> Thanks,
>>
>> Matt
>>
>>
>> 0 KSP unpreconditioned resid norm 4.038466809302e-03 true
>> resid norm 4.038466809302e-03 ||r(i)||/||b|| 1.000000000000e+00
>> Residual norms for fieldsplit_1_ solve.
>> 0 KSP preconditioned resid norm 0.000000000000e+00 true
>> resid norm 0.000000000000e+00 ||r(i)||/||b|| -nan
>> Linear fieldsplit_1_ solve converged due to CONVERGED_ATOL
>> iterations 0
>> 1 KSP unpreconditioned resid norm 4.860095964831e-06 true
>> resid norm 4.860095964831e-06 ||r(i)||/||b|| 1.203450763452e-03
>> Residual norms for fieldsplit_1_ solve.
>> 0 KSP preconditioned resid norm 2.965546249872e+08 true
>> resid norm 1.000000000000e+00 ||r(i)||/||b|| 1.000000000000e+00
>> 1 KSP preconditioned resid norm 1.347596594634e+08 true
>> resid norm 3.599678801575e-01 ||r(i)||/||b|| 3.599678801575e-01
>> 2 KSP preconditioned resid norm 5.913230136403e+07 true
>> resid norm 2.364916760834e-01 ||r(i)||/||b|| 2.364916760834e-01
>> 3 KSP preconditioned resid norm 4.629700028930e+07 true
>> resid norm 1.984444715595e-01 ||r(i)||/||b|| 1.984444715595e-01
>> 4 KSP preconditioned resid norm 3.804431276819e+07 true
>> resid norm 1.747224559120e-01 ||r(i)||/||b|| 1.747224559120e-01
>> 5 KSP preconditioned resid norm 3.178769422140e+07 true
>> resid norm 1.402254864444e-01 ||r(i)||/||b|| 1.402254864444e-01
>> 6 KSP preconditioned resid norm 2.648669043919e+07 true
>> resid norm 1.191164310866e-01 ||r(i)||/||b|| 1.191164310866e-01
>> 7 KSP preconditioned resid norm 2.203522108614e+07 true
>> resid norm 9.690500018007e-02 ||r(i)||/||b|| 9.690500018007e-02
>> <...>
>> 422 KSP preconditioned resid norm 2.984888715147e-02 true
>> resid norm 8.598401046494e-11 ||r(i)||/||b|| 8.598401046494e-11
>> 423 KSP preconditioned resid norm 2.638419658982e-02 true
>> resid norm 7.229653211635e-11 ||r(i)||/||b|| 7.229653211635e-11
>> Linear fieldsplit_1_ solve converged due to CONVERGED_RTOL
>> iterations 423
>> 2 KSP unpreconditioned resid norm 3.539889585599e-16 true
>> resid norm 3.542279617063e-16 ||r(i)||/||b|| 8.771347603759e-14
>> Linear solve converged due to CONVERGED_RTOL iterations 2
>>
>>
>> Does the slow convergence of the Schur block mean that my
>> preconditioning matrix Sp is a poor choice?
>>
>> Thanks,
>> David
>>
>>
>> On 06/11/2017 08:53 AM, Matthew Knepley wrote:
>>> On Sat, Jun 10, 2017 at 8:25 PM, David Nolte
>>> <dnolte at dim.uchile.cl <mailto:dnolte at dim.uchile.cl>> wrote:
>>>
>>> Dear all,
>>>
>>> I am solving a Stokes problem in 3D aorta geometries,
>>> using a P2/P1
>>> finite elements discretization on tetrahedral meshes
>>> resulting in
>>> ~1-1.5M DOFs. Viscosity is uniform (can be adjusted
>>> arbitrarily), and
>>> the right hand side is a function of noisy measurement data.
>>>
>>> In other settings of "standard" Stokes flow problems I
>>> have obtained
>>> good convergence with an "upper" Schur complement
>>> preconditioner, using
>>> AMG (ML or Hypre) on the velocity block and
>>> approximating the Schur
>>> complement matrix by the diagonal of the pressure mass
>>> matrix:
>>>
>>> -ksp_converged_reason
>>> -ksp_monitor_true_residual
>>> -ksp_initial_guess_nonzero
>>> -ksp_diagonal_scale
>>> -ksp_diagonal_scale_fix
>>> -ksp_type fgmres
>>> -ksp_rtol 1.0e-8
>>>
>>> -pc_type fieldsplit
>>> -pc_fieldsplit_type schur
>>> -pc_fieldsplit_detect_saddle_point
>>> -pc_fieldsplit_schur_fact_type upper
>>> -pc_fieldsplit_schur_precondition user # <--
>>> pressure mass matrix
>>>
>>> -fieldsplit_0_ksp_type preonly
>>> -fieldsplit_0_pc_type ml
>>>
>>> -fieldsplit_1_ksp_type preonly
>>> -fieldsplit_1_pc_type jacobi
>>>
>>>
>>> 1) I always recommend starting from an exact solver and
>>> backing off in small steps for optimization. Thus
>>> I would start with LU on the upper block and GMRES/LU
>>> with toelrance 1e-10 on the Schur block.
>>> This should converge in 1 iterate.
>>>
>>> 2) I don't think you want preonly on the Schur system. You
>>> might want GMRES/Jacobi to invert the mass matrix.
>>>
>>> 3) You probably want to tighten the tolerance on the Schur
>>> solve, at least to start, and then slowly let it out. The
>>> tight tolerance will show you how effective the
>>> preconditioner is using that Schur operator. Then you can start
>>> to evaluate how effective the Schur linear sovler is.
>>>
>>> Does this make sense?
>>>
>>> Thanks,
>>>
>>> Matt
>>>
>>>
>>> In my present case this setup gives rather slow
>>> convergence (varies for
>>> different geometries between 200-500 or several
>>> thousands!). I obtain
>>> better convergence with
>>> "-pc_fieldsplit_schur_precondition selfp"and
>>> using multigrid on S, with "-fieldsplit_1_pc_type ml" (I
>>> don't think
>>> this is optimal, though).
>>>
>>> I don't understand why the pressure mass matrix approach
>>> performs so
>>> poorly and wonder what I could try to improve the
>>> convergence. Until now
>>> I have been using ML and Hypre BoomerAMG mostly with
>>> default parameters.
>>> Surely they can be improved by tuning some parameters.
>>> Which could be a
>>> good starting point? Are there other options I should
>>> consider?
>>>
>>> With the above setup (jacobi) for a case that works
>>> better than others,
>>> the KSP terminates with
>>> 467 KSP unpreconditioned resid norm 2.072014323515e-09
>>> true resid norm
>>> 2.072014322600e-09 ||r(i)||/||b|| 9.939098100674e-09
>>>
>>> You can find the output of -ksp_view below. Let me know
>>> if you need more
>>> details.
>>>
>>> Thanks in advance for your advice!
>>> Best wishes
>>> David
>>>
>>>
>>> KSP Object: 1 MPI processes
>>> type: fgmres
>>> GMRES: restart=30, using Classical (unmodified)
>>> Gram-Schmidt
>>> Orthogonalization with no iterative refinement
>>> GMRES: happy breakdown tolerance 1e-30
>>> maximum iterations=10000
>>> tolerances: relative=1e-08, absolute=1e-50,
>>> divergence=10000.
>>> right preconditioning
>>> diagonally scaled system
>>> using nonzero initial guess
>>> using UNPRECONDITIONED norm type for convergence test
>>> PC Object: 1 MPI processes
>>> type: fieldsplit
>>> FieldSplit with Schur preconditioner, factorization
>>> UPPER
>>> Preconditioner for the Schur complement formed from
>>> user provided matrix
>>> Split info:
>>> Split number 0 Defined by IS
>>> Split number 1 Defined by IS
>>> KSP solver for A00 block
>>> KSP Object: (fieldsplit_0_) 1 MPI processes
>>> type: preonly
>>> maximum iterations=10000, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using NONE norm type for convergence test
>>> PC Object: (fieldsplit_0_) 1 MPI processes
>>> type: ml
>>> MG: type is MULTIPLICATIVE, levels=5 cycles=v
>>> Cycles per PCApply=1
>>> Using Galerkin computed coarse grid matrices
>>> Coarse grid solver -- level
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_coarse_) 1 MPI
>>> processes
>>> type: preonly
>>> maximum iterations=10000, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using NONE norm type for convergence test
>>> PC Object: (fieldsplit_0_mg_coarse_)
>>> 1 MPI
>>> processes
>>> type: lu
>>> LU: out-of-place factorization
>>> tolerance for zero pivot 2.22045e-14
>>> using diagonal shift on blocks to prevent
>>> zero pivot
>>> [INBLOCKS]
>>> matrix ordering: nd
>>> factor fill ratio given 5., needed 1.
>>> Factored matrix follows:
>>> Mat Object: 1 MPI
>>> processes
>>> type: seqaij
>>> rows=3, cols=3
>>> package used to perform
>>> factorization: petsc
>>> total: nonzeros=3, allocated nonzeros=3
>>> total number of mallocs used during
>>> MatSetValues
>>> calls =0
>>> not using I-node routines
>>> linear system matrix = precond matrix:
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=3, cols=3
>>> total: nonzeros=3, allocated nonzeros=3
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> Down solver (pre-smoother) on level 1
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_1_) 1
>>> MPI processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_1_) 1
>>> MPI processes
>>> type: sor
>>> SOR: type = local_symmetric, iterations =
>>> 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=15, cols=15
>>> total: nonzeros=69, allocated nonzeros=69
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down solver
>>> (pre-smoother)
>>> Down solver (pre-smoother) on level 2
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_2_) 1
>>> MPI processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_2_) 1
>>> MPI processes
>>> type: sor
>>> SOR: type = local_symmetric, iterations =
>>> 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=304, cols=304
>>> total: nonzeros=7354, allocated nonzeros=7354
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down solver
>>> (pre-smoother)
>>> Down solver (pre-smoother) on level 3
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_3_) 1
>>> MPI processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_3_) 1
>>> MPI processes
>>> type: sor
>>> SOR: type = local_symmetric, iterations =
>>> 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=30236, cols=30236
>>> total: nonzeros=2730644, allocated
>>> nonzeros=2730644
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down solver
>>> (pre-smoother)
>>> Down solver (pre-smoother) on level 4
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_4_) 1
>>> MPI processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_4_) 1
>>> MPI processes
>>> type: sor
>>> SOR: type = local_symmetric, iterations =
>>> 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: (fieldsplit_0_)
>>> 1 MPI
>>> processes
>>> type: seqaij
>>> rows=894132, cols=894132
>>> total: nonzeros=70684164, allocated
>>> nonzeros=70684164
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down solver
>>> (pre-smoother)
>>> linear system matrix = precond matrix:
>>> Mat Object: (fieldsplit_0_) 1 MPI
>>> processes
>>> type: seqaij
>>> rows=894132, cols=894132
>>> total: nonzeros=70684164, allocated
>>> nonzeros=70684164
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> KSP solver for S = A11 - A10 inv(A00) A01
>>> KSP Object: (fieldsplit_1_) 1 MPI processes
>>> type: preonly
>>> maximum iterations=10000, initial guess is zero
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using NONE norm type for convergence test
>>> PC Object: (fieldsplit_1_) 1 MPI processes
>>> type: jacobi
>>> linear system matrix followed by preconditioner
>>> matrix:
>>> Mat Object: (fieldsplit_1_) 1 MPI
>>> processes
>>> type: schurcomplement
>>> rows=42025, cols=42025
>>> Schur complement A11 - A10 inv(A00) A01
>>> A11
>>> Mat Object: (fieldsplit_1_)
>>> 1
>>> MPI processes
>>> type: seqaij
>>> rows=42025, cols=42025
>>> total: nonzeros=554063, allocated
>>> nonzeros=554063
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> A10
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=42025, cols=894132
>>> total: nonzeros=6850107, allocated
>>> nonzeros=6850107
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> KSP of A00
>>> KSP Object: (fieldsplit_0_)
>>> 1
>>> MPI processes
>>> type: preonly
>>> maximum iterations=10000, initial guess
>>> is zero
>>> tolerances: relative=1e-05, absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using NONE norm type for convergence test
>>> PC Object: (fieldsplit_0_)
>>> 1
>>> MPI processes
>>> type: ml
>>> MG: type is MULTIPLICATIVE, levels=5
>>> cycles=v
>>> Cycles per PCApply=1
>>> Using Galerkin computed coarse grid
>>> matrices
>>> Coarse grid solver -- level
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_coarse_) 1 MPI processes
>>> type: preonly
>>> maximum iterations=10000, initial
>>> guess is zero
>>> tolerances: relative=1e-05,
>>> absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using NONE norm type for convergence
>>> test
>>> PC Object:
>>> (fieldsplit_0_mg_coarse_) 1 MPI processes
>>> type: lu
>>> LU: out-of-place factorization
>>> tolerance for zero pivot 2.22045e-14
>>> using diagonal shift on blocks to
>>> prevent zero
>>> pivot [INBLOCKS]
>>> matrix ordering: nd
>>> factor fill ratio given 5., needed 1.
>>> Factored matrix follows:
>>> Mat Object:
>>> 1 MPI
>>> processes
>>> type: seqaij
>>> rows=3, cols=3
>>> package used to perform
>>> factorization: petsc
>>> total: nonzeros=3, allocated
>>> nonzeros=3
>>> total number of mallocs used
>>> during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> linear system matrix = precond matrix:
>>> Mat Object: 1
>>> MPI processes
>>> type: seqaij
>>> rows=3, cols=3
>>> total: nonzeros=3, allocated
>>> nonzeros=3
>>> total number of mallocs used
>>> during MatSetValues
>>> calls =0
>>> not using I-node routines
>>> Down solver (pre-smoother) on level 1
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_1_) 1 MPI
>>> processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05,
>>> absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence
>>> test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_1_) 1 MPI
>>> processes
>>> type: sor
>>> SOR: type = local_symmetric,
>>> iterations = 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: 1
>>> MPI processes
>>> type: seqaij
>>> rows=15, cols=15
>>> total: nonzeros=69, allocated
>>> nonzeros=69
>>> total number of mallocs used
>>> during MatSetValues
>>> calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down
>>> solver (pre-smoother)
>>> Down solver (pre-smoother) on level 2
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_2_) 1 MPI
>>> processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05,
>>> absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence
>>> test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_2_) 1 MPI
>>> processes
>>> type: sor
>>> SOR: type = local_symmetric,
>>> iterations = 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: 1
>>> MPI processes
>>> type: seqaij
>>> rows=304, cols=304
>>> total: nonzeros=7354, allocated
>>> nonzeros=7354
>>> total number of mallocs used
>>> during MatSetValues
>>> calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down
>>> solver (pre-smoother)
>>> Down solver (pre-smoother) on level 3
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_3_) 1 MPI
>>> processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05,
>>> absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence
>>> test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_3_) 1 MPI
>>> processes
>>> type: sor
>>> SOR: type = local_symmetric,
>>> iterations = 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object: 1
>>> MPI processes
>>> type: seqaij
>>> rows=30236, cols=30236
>>> total: nonzeros=2730644, allocated
>>> nonzeros=2730644
>>> total number of mallocs used
>>> during MatSetValues
>>> calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down
>>> solver (pre-smoother)
>>> Down solver (pre-smoother) on level 4
>>> -------------------------------
>>> KSP Object:
>>> (fieldsplit_0_mg_levels_4_) 1 MPI
>>> processes
>>> type: richardson
>>> Richardson: damping factor=1.
>>> maximum iterations=2
>>> tolerances: relative=1e-05,
>>> absolute=1e-50,
>>> divergence=10000.
>>> left preconditioning
>>> using nonzero initial guess
>>> using NONE norm type for convergence
>>> test
>>> PC Object:
>>> (fieldsplit_0_mg_levels_4_) 1 MPI
>>> processes
>>> type: sor
>>> SOR: type = local_symmetric,
>>> iterations = 1, local
>>> iterations = 1, omega = 1.
>>> linear system matrix = precond matrix:
>>> Mat Object:
>>> (fieldsplit_0_) 1 MPI processes
>>> type: seqaij
>>> rows=894132, cols=894132
>>> total: nonzeros=70684164,
>>> allocated nonzeros=70684164
>>> total number of mallocs used
>>> during MatSetValues
>>> calls =0
>>> not using I-node routines
>>> Up solver (post-smoother) same as down
>>> solver (pre-smoother)
>>> linear system matrix = precond matrix:
>>> Mat Object:
>>> (fieldsplit_0_) 1 MPI processes
>>> type: seqaij
>>> rows=894132, cols=894132
>>> total: nonzeros=70684164, allocated
>>> nonzeros=70684164
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> A01
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=894132, cols=42025
>>> total: nonzeros=6850107, allocated
>>> nonzeros=6850107
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=42025, cols=42025
>>> total: nonzeros=554063, allocated nonzeros=554063
>>> total number of mallocs used during
>>> MatSetValues calls =0
>>> not using I-node routines
>>> linear system matrix = precond matrix:
>>> Mat Object: 1 MPI processes
>>> type: seqaij
>>> rows=936157, cols=936157
>>> total: nonzeros=84938441, allocated nonzeros=84938441
>>> total number of mallocs used during MatSetValues
>>> calls =0
>>> not using I-node routines
>>>
>>>
>>>
>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin
>>> their experiments is infinitely more interesting than any
>>> results to which their experiments lead.
>>> -- Norbert Wiener
>>>
>>> http://www.caam.rice.edu/~mk51/
>>> <http://www.caam.rice.edu/%7Emk51/>
>>
>>
>>
>>
>> --
>> What most experimenters take for granted before they begin their
>> experiments is infinitely more interesting than any results to
>> which their experiments lead.
>> -- Norbert Wiener
>>
>> http://www.caam.rice.edu/~mk51/ <http://www.caam.rice.edu/%7Emk51/>
>
>
>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which
> their experiments lead.
> -- Norbert Wiener
>
> http://www.caam.rice.edu/~mk51/ <http://www.caam.rice.edu/%7Emk51/>
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